The purpose of this thesis has been to calculate and implement the Arnold-Winther elasticity elements with strongly imposed symmetry. The next aim has been to investigate the research question: Will mixed finite element method (MxFEM) result in more detailed plots of solutions when discontinuous Lamè constants are involved, than what the Galerkin finite element method (FEM) would give?
The background for the research question is that MxFEM results in more detailed plots of solutions than FEM in fluid flow when there is a discontinuous coefficient. It is therefore interesting to see if this also happens in another elliptic equation, in particular the elasticity equation. Moreover, the general motivation for applying MxFEM on elasticity is that some elasticity models, for instance the visco-elasticity, are complex and cannot be reduced to one equation such that FEM can be applied.
The implementation of the Arnold-Winther elements and the elasticity simulator has been done in Diffpack. Diffpack is an object-oriented software package in C++ for developing numerical software for solving partial differential equations.
Error calculations and rate of convergence verify the implemented elasticity simulator. The numerical simulations with discontinuous Lamè constants are presented through plots of the solutions. These plots are discussed, and the concluding answer to the research question is that MxFEM does indeed give more detailed solutions in elasticity with discontinuous elasticity constants than FEM.